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ICSE-VIII-Mathematics

01: Rational Numbers Class 8 Maths

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    Section : A
    Exercise 1(A)
  • Qstn #1
    Add, each pair of rational numbers, given below, and show that their addition (sum) is also a rational number:
  • #1-i
    -5/8 and 3/8
    Ans : (-5)/8 and 3/8
    = (-5)/8 + 3/8
    (∵ Denominators are same, ∴ LCM = 8)
    = (-5 + 3)/8
    = (-2)/8 = (-1)/4
    Which is a rational number.
  • #1-ii
    -8/13 and -4/13
    Ans : (-8)/13 and (-4)/13
    = (-8)/13 + (-4)/13
    (∵ LCM of 13 and 13 = 13)
    = (- 8 - 4)/13 = (-12)/13
    Which is a rational number.
  • #1-iii
    6/11 and -9/11
    Ans : 6/11 and (-9)/11
    = 6/11 + (-9)/11
    (∵ Denominator are same, ∴ LCM = 11)
    = (6 - 9)/11 = (-3)/11
    Which is a rational number.
  • #1-iv
    5/-26 and 8/39
    Ans : 5/(-26) and 8/39
    = 5/(-26) + 8/39
    = (-5 × 3)/(26 × 3) + (8 × 2)/(39 × 2)
    ∴ LCM of 26 and 39 = 2 × 3 × 13 = 78
    = (-15 + 16)/78 (∵ LCM of 26 and 39 = 78)
    = 1/78
    Which is a rational number.
  • #1-v
    5/-6 and 2/3
    Ans : 5/(-6) and 2/3
    = (-5)/6 + 2/3
    ∴ LCM of 6, 3 = 2 × 3 = 6
    = (-5 × 1)/(6×1) + (2 × 2)/(3 × 2)
    (∵ LCM of 6 and 3 = 6)
    = (-5 + 4)/6 = (-1)/6
    Which is a rational number.
  • #1-vi
    -2 and 2/5
    Ans : (-2) and 2/5
    = (-2)/1 + 2/5 (∵ LCM of 1 and 5 = 5)
    = (-2 × 5)/(1 × 5) + (2 × 1)/(5 × 1)
    = (-10 + 2)/5 = (-8)/5
    Which is a rational number.
  • #1-vii
    9/-4 and -3/8
    Ans : 9/-(4) and (-3)/8
    = (-9)/4 + (-3)/8
    ∴ LCM of 4 and 8 = 2 × 2 × 2 = 8
    = (-9 × 2)/(4 × 2) - (3 × 1)/(8 × 1)
    (∵ LCM of 4 and 8 = 8)
    = (- 18 - 3)/8 = (-21)/8
    Which is a rational number.
  • #1-viii
    7/-18 and 8/27
    Ans : 7/(-18) and 8/27
    = 7/(-18) + 8/27
    = (-7 × 3)/(18 × 3) + (8 × 2)/(27 × 2)
    ∴ LCM of 18 and 27 = 2 × 3 × 3 × 3 = 54
    = (-21 + 16)/54 = (-5/54)
    Which is rational number.
  • #2-i
    5/9 + -7/6
    Ans : 5/9 + (-7)/6
    ∴ LCM of 9 and 6 = 2 × 3 × 3 = 18
    = (5 × 2)/(9 × 2) - (7 × 3)/(6 × 3)
    (∵ LCM of 9 and 6 = 18)
    = (10 - 21)/18 = -11/8
  • #2-ii
    4 + 3/-5
    Ans : 4 + 3/(-5)
    = 4/1 + 3/(-5)
    = 4/1 - 3/5
    = (4 × 5)/(1 × 5) - (3 × 1)/(5 × 1)
    (∵ LCM 1 and 5 = 5)
    = (20 - 3)/5 = 17/5 = 3.2/5
  • #2-iii
    1/-15 + 5/-12
    Ans : 1/(-15) + 5/(-12)
    = (-1)/15 + (5/-12)
    = (-1)/15 - 5/12
    ∴ LCM of 15 and 12 = 2 × 2 × 3 × 5 = 60
    = (-1 × 4)/(15 × 4) - (5 × 5)/(12 × 5)
    (∵ LCM of 15 and 12 = 60)
    = (-1 × 4)/(15 × 4) - (5 × 5)/(12 × 5)
    (∵ LCM of 15 and 12 = 60)
    = (-4 - 25)/60 = -29/60
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